"Trading is statistics and time series analysis." This blog details my progress in developing a systematic trading system for use on the futures and forex markets, with discussion of the various indicators and other inputs used in the creation of the system. Also discussed are some of the issues/problems encountered during this development process. Within the blog posts there are links to other web pages that are/have been useful to me.

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Tuesday, 28 February 2012

I have just read an interesting blog post here which could be seen as a possible confirming factor for my prediction (my previous post) of a retracement in the S&P and consequent run-up or volatility in gold.

Monday, 27 February 2012

I'm not going to make a habit of posting all solutions as I complete the coding and deployment of them, but I thought readers might be interested in the Delta solution for gold (gc) shown below.

It's interesting because, according to Delta, gold is now in its inversion window on the MTD time frame, shown on the above chart as the two solid red vertical lines. By my count the first MTD red line marks a low, the green MTD a high point 1, followed by a possible in-between-point (IBP), which if it holds means higher prices are indicated for the high MTD point 2 in about 2 to 4 weeks time. However, at that time the ITD time frame will be in its inversion window too. Delta theory says that big moves can be expected around point 1 (in the inversion time window) and here we have two inversion time windows coinciding! Gold may very well experience some big move or increased volatility in the next few weeks, maybe as a result of a flight to safety from the unusual recent run-up in the S&P (see the chart in my previous post) and its impending correction. I look forward to seeing how this interpretation based on Delta pans out.

Sunday, 26 February 2012

This post will be the last in this series that tests the Delta Phenomenon, and acts as a summary of the previous posts. Part 1 talks about the "breakthrough" R coding that made the series of tests possible, part 2 was a general discussion about the subjectiveness of Delta, part 3 introduced the methodology of my statistical tests of Delta, with R code of the test routine, parts 4 & 5 present the results of the tests on the S&P 500 MTD solution, and part 6 the results of the ITD solution. The final results in posts 4, 5 & 6 mean that the null hypothesis of no predictive ability for Delta can be rejected, and thus the alternative hypothesis of Delta having predictive ability is accepted.

One should be cautioned, however, that statistical significance is not necessarily of practical significance, and perhaps one should ask why the Delta Phenomenon should work at all? A lot of the criticism I have read on forums etc. obviously relates to the difficulty of actually using Delta in trading. Another theme of criticism relates to the supposed "astrological" aspect of Delta and therefore some rather dismissive comments relegating Delta to the realm of crystal-ball gazing, mumbo-jumbo. I think this second form of criticism is ill-founded and rather ignorant. If you think about it, the interaction of the Sun and Earth, the phases of the moon etc. are just another way of saying "seasonality" and I think it is pretty well accepted that there is seasonality in, for example, agricultural commodity futures, oil futures etc. This seasonality may well be reflected in the share prices/indices by the linkage of large commercial interests in these areas, and various knock-on effects in trade, currency movements etc. My take on Delta is that it can be regarded as a sophisticated form of seasonal analysis, and all the normal caveats that would apply to trading seasonal tendencies should also apply to Delta.

Accepting that there could be some reasonable fundamental justification for Delta and that it has been shown to be statistically significant in terms of its accuracy as described by the methodology, how does one actually trade it? Some guidelines might be gleaned from these sample reports from a Delta timing service. Reading these sample reports shows how a knowledge of Delta can be used to draw inferences from current market action and to perhaps formulate a suitable trading strategy. Of course, analysis such as this is not a 100% mechanical approach, but it may very well add real value to the bottom line.

Given this, I have decided to deploy all the other Delta solutions I have to create Delta Charts that look like this

where the solid vertical lines are the MTD solution and the dashed the ITD solution. Doing this across the 30 or so commodities I regularly track will probably take me a few weeks. Once done, I will think about how to combine Delta with the other indicators I have mentioned in previous posts and test a trading system based on them. More in due course.

Sunday, 19 February 2012

I have now finished the testing of the Intermediate Term solution for the S&P 500 and summary results are shown below, giving the test period for each separate test conducted (15 in total) along with the test statistic of the actual data and the p-value percentage, which should be read as the percentage of random permutations (500,000 in total for each test) that were as good as or better than the actual test statistic in question for that period. The period for each test covers the time span for one complete cycle of the solution, i.e. from point 1 to point 12 of the solution. The entire test period more or less corresponds with the period for the earlier Medium Term solution tests, and as in those previous tests, the data for the period is out of sample data, i.e. not "seen" by the solution prior to the tests being conducted.

As can be seen, if 5 % is taken as the level of statistical significance only one test fails to reject the null hypothesis, and 7 out of the remaining 14 are statistically significant at the 1 % level. I also repeated the test several times over the entire data period, encompassing a total of 182 separate turning points with a test statistic of 4.10989 for these 182 points. In these repeated tests (for a total of a few million permutations) not a single permutation was as good as or better than the given test statistic! These results are much better than I had anticipated and I therefore consider Delta to have passed these tests as well. For readers' interest a plot of the period in which the null hypothesis is not rejected is shown below,

where the yellow lines are my identification of the actual turning points and the white, red and green lines are the turning points projected by the solution.

Now that this series of tests is complete, and Delta has passed them, what does it all mean? This will be the subject of my next post.

I'm not quite sure how it happened, but I've missed the opportunity to take part in the Delta training sessions that I mentioned in my previous post. I installed an IRC client and went to the forex #training channel and was able to download the course materials from a linked Skydrive account, but on the day the training began I couldn't access the #training channel. In hindsight it may have been due to my unfamiliarity with the IRC client (this was the first time I'd ever used IRC) and some confusion on my part with the various log messages. I contacted the #help channel and I was told that access to the training is now closed and there is no information about any repeat of the course. All in all, very disappointing.

Perhaps the anonymous reader who alerted me to the course in the first place has more information? I would be grateful to hear from you again.

Wednesday, 15 February 2012

...there is a Delta Phenomenon multi-week training session via IRC by a group of DP experts!.. The classes are Monday, Wednesday and Friday 2-5pm EST starting on February 16th. irc server irc.forex.com #training

I shall try to attend these training sessions, and look forward to them.

Monday, 13 February 2012

The first round of tests, consisting of tests of the Medium Term Solution for the S & P 500, is now complete and the summary results are given below.

Years 2007 to 2008 - 16th Aug 2007 to 6th Jan 2009 incl.
[1] 9.722222 - test statistic, the average error of identified turns, in days
[1] 103 - number of random permutations as good as or better than test stat
[1] 0.0206 - above expressed as % of permutations, the p-value
[1] 37.6425 - average of permutation error distribution, in days
[1] 16.32295 - standard deviation of permutation error distribution, in days
[1] 1.710493 - test statistic distance from average of permutation error distribution, expressed as a multiple of standard deviation of permutation error distribution

Year 2009 - 20th Dec 2008 to 16th Jan 2010 incl.
[1] 10.42857 - test statistic, the average error of identified turns, in days
[1] 809 - number of random permutations as good as or better than test stat
[1] 0.1618 - above expressed as % of permutations, the p-value
[1] 33.43553 - average of permutation error distribution, in days
[1] 14.18181 - standard deviation of permutation error distribution, in days
[1] 1.622286 - test statistic distance from average of permutation error distribution, expressed as a multiple of standard deviation of permutation error distribution

Year 2010 - 27th Nov 2009 to 28th Jan 2011 incl.
[1] 11.35714 - test statistic, the average error of identified turns, in days
[1] 1706 - number of random permutations as good as or better than test stat
[1] 0.3412 - above expressed as % of permutations, the p-value
[1] 34.92687 - average of permutation error distribution, in days
[1] 15.36711 - standard deviation of permutation error distribution, in days
[1] 1.533777 - test statistic distance from average of permutation error distribution, expressed as a multiple of standard deviation of permutation error distribution

All out of sample data - 16th Aug 2007 to 28th Jan 2012
[1] 9.8 - test statistic, the average error of identified turns, in days
[1] 0 - number of random permutations as good as or better than test stat
[1] 0 - above expressed as % of permutations, the p-value
[1] 67.47298 - average of permutation error distribution, in days
[1] 29.38267 - standard deviation of permutation error distribution, in days
[1] 1.962823 - test statistic distance from average of permutation error distribution, expressed as a multiple of standard deviation of permutation error distribution

The histogram plot of the final, all out of sample data

I think the results are unambiguous - given the consistently low p-values the null hypothesis can be rejected and the alternative hypothesis accepted i.e. the S & P 500 Medium term solution is NOT random and therefore has some predictive value.

My next round of tests will be of the Intermediate term solution for the S & P 500. Before conducting these tests however, I would like to state my expectation that the results will not be as conclusive as those given above. This is due to the fact that the Intermediate term solution also has 12 points, but these 12 points occur within a time period that is approximately 120 days long, so the actual average error on this time frame will have to be 2 or 3 bars/days or better to match the above results.

Sunday, 5 February 2012

The results of the first test are in! The test period approximately covers 2011, from 6th January 2011 to 12th January 2012 inclusive and the test was of the MTD Delta solution for the S&P 500. I chose the S&P 500 because I suppose that most readers would be interested in this market as a proxy for stock markets in general. There are 12 turning points in this solution and a screen shot is shown below.

The projected solution turning points are indicated with white, red and green lines whilst the actual turns in the data are indicated in yellow. For the purposes of counting, each yellow, actual turn line is paired with one of the projected solution lines, i.e. counting from the left the first yellow line is paired with the first white solution line, the second with the second, third with third etc. The red solution lines indicate the "inversion" window with the green line between them being the number 1 point of the solution.

The first thing that stands out is that the biggest move of the year occurred within the inversion time period window, and the Delta Phenomenon book states that big moves can be expected around the number 1 point (green line), so kudos to Delta so far. Another thing that stands out is that most turning points occur within one to two weeks of their projected turning points, well within the margin of error for this solution. Kudos plus 2 for Delta. However the litmus test is this

[1] 8.769231
[1] 278
[1] 0.0556
[1] 33.09061
[1] 14.54137
[1] 1.672565
the results of a 0.5 million random permutation test. With only 278 random permutations out of half a million matching or bettering the average error test statistic, giving a p-value of 0.0556%, the null hypothesis can be rejected at a statistical significance level of 0.1%. Delta has passed this first test.